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An Clockwork Physic

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Integral to the operation of the mechanical watch is the balance wheel. Balance wheels are constructed of a weighted wheel and a spiraled torsion hairspring. The wheel is composed of a metal alloy with low thermal expansion, and the spring is made of either steel or silicon. Energy stored in the watch's mainspring is translated through the gear train to the escapement, a trident shaped piece with a dedicated escapement wheel which delivers impulses to the balance wheel. The balance wheel is what allows a watch to run accurately, as the balance wheel functions as a harmonic oscillator due to the constant mass of the wheel and elasticity of the spring. Balance wheel oscillations are determined by the time taken to complete a semi-rotation, called a vibration. Balance wheel oscillations are usually within the range of 28,800 vph (vibrations per hour, or 4 Hz), which ticks 8 times per second. The period of oscillation T of a balance wheel (one oscillation, or two ticks) is determined by the equation, T=2π*√(I/k) where I is the moment of inertia of the balance wheel, and k is the spring constant of the torsional hairspring.


f5V5kAc.gif  Breguet-balance-wheel.jpg

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Very insightful! Watch design is all about physics, and the horological (the study of time keeping) world is rather obsessed with over-complicated watches. An interesting side note: watches can display any information that varies linearly in response to time. For example, some watches have moon-phase complications, showing the current state of the moon, and some even keep track of constellations. Also, there is a very intricate watch complication known as a 'tourbillon' (French for "Whirlwind"), in which the balance-wheel/escapement assembly is mounted in a three axis rotating cage (think 3-axis gimbal), which reduces the effects of gravity on the period of oscillation of the balance wheel, creating a more accurate timepiece.

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